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When I detected this brazen piracy, more than three decades after first hearing the songs, I was livid. I wanted to call up the lawyer that the Rolling Stones hired to sue the Verve for nicking the opening riff of The Last Time for their hit, Bittersweet Symphony. That lawsuit wrecked the Verve. I wanted the same blood from whatever nursery rhyme writer had plagiarised this beloved tune.

It gets worse. Louis Armstrong’s What a Wonderful World is basically the same too. Again, sing along: “I see trees of green, red roses too / How I wonder what you are / And I think to myself – YOU THIEF.”

I tested the theory out by singing all four songs to my three-year-old son at bedtime. “They’re the same, Daddy,” he said indignantly. “Sing me a diffewent song.”

So I started to investigate where it all started, looking into the melody’s history, and asking musician friends to explain its amazing steal-ability.

There’s a German Christmas carol, Morgen kommt der Weihnachtsmann, and a Dutch one too, Altijd is Kortjakje ziek.

Might the melody be so elemental that it could have emerged independently? I asked this question to Dr Katie Overy, senior lecturer in music at the University of Edinburgh. “Very unlikely,” she said. “It would have transferred orally because it’s a good tune. There’s a rich history in folk music of using the same melody with different words, and modern culture and technology has no doubt speeded up this transfer.”

The probability is that, as with the world’s other most recognisable tunes – Happy Birthday, Yesterday, Frère Jacques – the melody was composed in one place, by one or two people. It would then have spread virally, as in the recent movie Contagion, where a bat exchanges fluids with a pig which is then eaten by Gwyneth Paltrow, who contracts the deadly sickness, and triggers a chain reaction that kills millions.

I began my search for the source of this magical musical germ. I wanted to identify the creator, and alert them (or more probably their descendants) on how to gain the kudos and cash they deserved.

First stop was iTunes, which lists a whopping 2,200 versions of Twinkle, Twinkle. There are some great renditions, like Elizabeth Mitchell’s ethereal rendition; some terrible ones, like Olivia Newton John’s harp-dripping, saccharine abomination; and some innovative ones, like the Elegants’ rock ‘n roll singleLittle Star, that made #1 on the Billboard Hot 100 in 1958.

The song has been integrated into numerous classic songs, according to Gary Lucas, a legendary rock and jazz guitarist who co-wrote the song Grace with his protégé Jeff Buckley, and who worked as a composer on my film American Faust: From Condi to Neo Condi.

“It’s created a lyrical theme,” Lucas says. “Listen to the Stanley Brothers’ great bluegrass track Little Maggie, whose eyes ‘shine like a diamond in the sky.’ Or even Lucy in the Sky with Diamonds, where John Lennon is psychedelically playing with pattern recognition. It’s there again in Instant Karma, where 'we all shine on like the moon and the stars'. Melodically, it’s there in Kraftwerk’s Autobahn, or my own cover version, where I riff on the descending scale of “like a diamond in the sky”.

Whether explicitly or subliminally referenced, all these songs mark the author of the melody as ‘unknown’. So I had to hunt further back in history. My father told me of how he had come across a Latin version in the 1950s: “Mica, mica, parva stella, / Miror quaenam sis tam bella. /Super terra in caelo, / Alba gemma splendido". The first appearance of this version was in an 1894 book, When Life is Young, by Mary Mapes Dodge.

Pushing further into the 19th century, I opened up 1865’s Alice in Wonderland, where the Mad Hatter parodies the song at his tea party: “Twinkle, twinkle, little bat! / How I wonder what you're at! / Up above the world you fly, / Like a tea tray in the sky.”

I then discovered the first occasion when the melody was exploited as an advertising jingle. Around 1845, a Scottish man called Robert Coltard concocted an aniseed-flavoured sweet called Coulter’s Candy, and promoted it to the Twinkle melody and these lyrics: “Ally bally, ally bally bee, / Sittin' on yer mammy's knee, / Greetin' for a wee bawbee, / Tae buy mair Coulter's Candy.”

The song went on to become a classic Scottish folk song, and the sweet began to be remanufactured in 2009 by Dundee-based Ally Bally Bees Ltd. But again, no royalties from have ever been paid to our forgotten composer.

Commercial exploitation of the melody was also taking place across the pond. In 1835, Boston-based music publisher Charles Bradlee had the gall to copyright the song through an act of Congress. The lyrics he recorded were those of The Alphabet Song – as if the alphabet was copyrightable! More outrageously, he claimed ownership of the melody as “a German air with variations for the flute with an easy accompaniment for the piano forte". He did give some credit on the melody to a composer called Louis Le Maire, who had conveniently died in 1750. There is no other evidence that Le Maire wrote the melody, but Bradlee prospered handsomely from his copyright stake.

There is no mystery around who wrote the English words to Twinkle, Twinkle. It was a 23-year-old from Suffolk, England called Jane Taylor. In 1806, she wrote a poem called The Star which was published in a book called Rhymes for the Nursery.

There are actually five stanzas, which was a refreshing find, since the first one was getting tedious to have to sing it every night to my children. To share that discovery with any needy parents out there, verse two goes: “When the blazing sun is gone, / When he nothing shines upon, / Then you show your little light, / Twinkle, twinkle, all the night.”

The enigmatic verse five concludes the song: “As your bright and tiny spark, / Lights the traveller in the dark. / Though I know not what you are, / Twinkle, twinkle, little star.”

It’s not known exactly when this poem was joined with the melody, but the first published combo version was in 1838, in the book The Singing Master.

Jane Taylor, who died in 1866, is unlikely to have seen any proceeds from her creation, and certainly had no idea of the millions of children she would end up delighting. One consolation for her, should she be smiling down from the firmament, is that Star Trek: Enterprise honoured her by naming a character after her.

Continuing our journey to the source, we pause in 1833, when Franz Liszt first performed a melody called Ah vous dirai-je, Maman. But Mr Liszt openly admitted he was not the melody’s maker, but had heard it in the work of another grand master, Wolfgang Amadeus Mozart.

Many people still believe that Mozart composed the tune. What is true is that Mozart wrote twelve variations on the theme, also called Ah vous dirai-je, Maman, some time between 1782 and 1786, while he was staying in Paris.

But Mozart was himself knocking off the melody from a song called Le Faux Pas, whose first line was "Ah! vous dirai-je, Maman". Like Coulter’s Candy, it was also used to promote the good things in life: “Ah! I shall tell you, mummy,/ What causes me torment./Daddy wants me to reason/Like a grown-up./ But I say that sweeties / are worth more than reason.”

That ditty first appeared in 1761, when Mozart was just six, in a collection of traditional French songs called Les Amusements d'une Heure et Demy, by M. Bouin. Nothing more is known of Mr Bouin. In no history of music, could I find any evidence to suggest that he composed the melody, nor of where he found it.

The trail ended there.

Frustrated, I speculated the composer was some brilliant 16th-century Provençal milkmaid too committed to her secret art to record her work anywhere.

Gary Lucas disagreed: “I bet it was a Greek shepherd on a panpipe, playing from the dawn of the world. The panpipe would have had all the necessary notes.”

Whoever the piper was, I lamented s/he had not had the hindsight of the story of the two women who created the world’s other most recognisable song, Happy Birthday. In 1893, a kindergarten principal called Patty Hill started singing the Happy Birthday tune to her class in Kentucky. It was called Good Morning to All then, and many have claimed the melody itself was knocked off another song, Happy Greetings to All, by Horace Waters. Either way, the song was so popular that Patty and her composer sister Mildred published it in a songbook called Song Stories for the Kindergarten.

In 1924, the melody was published for the first time to Happy Birthday lyrics, although no one knows who set it to those words first. Commercial exploitation grew, with the song appearing in the 1931 Broadway musical The Band Wagon and a Western Union telegram commercial. When it featured in Irving Berlin’s As Thousands Cheer, a third Hill sister, Jessica, stepped in. She teamed up with a lawyer in 1934, and secured the copyright on the song for her two sisters.

Mildred was already dead by then. Jill would only have until 1946 to enjoy the proceeds of her creation before she too died, and both sisters had no children. But the Hill Trust, and their publishing partners, have profited handsomely. They sold the rights to Time-Warner Corporation in 1998, and their lawyers still enforce a law that demands that you buy a license if you want to use Happy Birthday in film, TV, radio, or anywhere open to the public. In 2008, the song yielded over $2 million in royalties, and this revenue stream will continue until copyright runs out in 2030 in the USA, and 2016 in the EU.

And that’s all for a melody that might well have been composed by Horace Waters, a man just as uncompensated as the piper who first played Twinkle'’s melody.

I asked Carol Connors, a Hollywood songwriter who was Oscar-nominated for composing the theme songs for Rocky and The Rescuers’ how she felt towards the piper: “Plagiarism is nothing new,” she shrugged. “We don’t always know what we’re stealing. I wrote a hit record for the Ripchords called Hey Little Cobra, and it went on to become the most important hot-rod song ever. But a UCLA musicologist later showed me I had taken the tune from a song called Mama’s Little Baby Loves Short’nin’ Bread. It was public domain, so we were okay.”

With the trail dead on the piper’s identity, the only way I could really honor her was to shed light on the melody itself. What makes this tune so universally cherished?

To answer that, I needed to understand the mechanics of the song, and how it stimulates our minds. Since I was never even close to taking grade one piano, I had to interview some real musicians and musicologists.

Dr Overy, who specialises in music and brain function, pinpoints three attributes behind the song’s success: “First, it’s singable – it’s in a small range, it’s in 4/4 time, in a major key, and has a well-shaped melody, with leaps up perfect 4ths and 5ths, followed by simple step-by-step movements down again. Second, it’s memorable. It has an A-B-A structure, which gives the song its own narrative. That narrative has a lot of repetition in it, which helps make a song stick in the brain. And third, it’s interesting, both for musicians like Mozart because of its implied harmonies, and for the listener, because the melody has inherent tension in it. The ‘up above the world so high’ and ‘like a diamond in the sky’ lines are unfinished, not quite reaching the bottom. That builds tension, which makes it interesting even for adults.”

Matt Peacock, a musician whose work producing opera performed by homeless people recently earned him an MBE, celebrates the song’s deceptive simplicity: “It’s one of the easiest tunes to play on a kiddie’s xylophone – the ones with different colours for each key – since it fits nicely into a single octave. It’s also really simple with the opening figure repeated at the end and a second figure repeated twice in the middle. All the best music has simplicity at its heart – usually with layers of complexity underneath. Take Mozart, Bach, Britten – all geniuses who could write a damn good tune!”

Carol Connors, whose song To Know Him is to Love Himwas one of the catchiest songs of the 20th century, says, “Twinkle, Twinkle is the ultimate hit. I learned what a ‘hit’ is from Berry Gordy, the founder of Motown records who once told me: ‘A hit record is repetition. If it was a hit, it was infectious; if it was a miss, it was monotonous.’ There ain’t nothing monotonous about Twinkle, Twinkle.”

David Wolfert, who has written hit songs for Whitney Houston, Barbra Streisand and Cher, and who composed the score for my film True Bromancesays: “Our enjoyment of music is based on a combination of the tune going where we are culturally conditioned to expect it to go, and how it surprises us from time to time by not doing what we expect. Children like the more expected musical path. This tune, which starts on the first degree of the scale, or tonic – C in the key of C – then comes to rest on the fifth step of the scale on the word ‘star’. The fifth step – G in the key of C – is known to be the second strongest step to our Western ears. The tune then returns to the tonic again on the word ‘are’, which satisfies our expectation of completion.”

Gary Lucas crystallises how this satisfaction enters our ears and hearts: “The song goes up and down, like life does. It’s a comforting revolution. Kids love it because they want to be clinging to mama’s heartbeat. This gives them that heartbeat. It’s a question and answer that’s gracefully resolved. It’s a mantra, like Don’t Worry, be Happy. It’s a song about the infinite. It makes us feel good; it shows that we’re all eternal, that we all shine on. It’s oral bubblegum that comes from the origin of music, from the piper at the gates of dawn. It’s an anthem, a hypnotic call for children of all ages to play.”

It is that power that explains why this extraordinary melody has echoed through so many places and times – and why so many musicians have been tempted to pinch it.